Boundedness of Fourier integral operators on Fourier Lebesgue spaces and affine fibrations

• Autorzy: Fabio Nicola
• Języki publikacji: EN

Abstrakty

EN

We study Fourier integral operators of Hörmander's type acting on the spaces $ℱL^{p}(ℝ^{d})_{comp}$, 1 ≤ p ≤ ∞, of compactly supported distributions whose Fourier transform is in $L^{p}$. We show that the sharp loss of derivatives for such an operator to be bounded on these spaces is related to the rank r of the Hessian of the phase Φ(x,η) with respect to the space variables x. Indeed, we show that operators of order m = -r|1/2-1/p| are bounded on $ℱ L^{p}(ℝ^{d})_{comp}$ if the mapping $x ↦ ∇_{x}Φ(x,η)$ is constant on the fibres, of codimension r, of an affine fibration.

Kategorie tematyczne

• 35S30: Fourier integral operators
• 42B35: Function spaces arising in harmonic analysis

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 198
• Numer: 3
• Strony: 207-219

Daty

wydano

2010

Twórcy

autor

Fabio Nicola

• Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Identyfikatory

DOI

10.4064/sm198-3-1